SEATTLE — Hundreds of same-sex couples across Washington state started picking up marriage licenses Thursday as a voter-approved law legalizing gay marriage took effect.

King County, the state’s largest, opened the doors to its auditor’s office in Seattle just after midnight to start distributing licenses. But hundreds of people had lined up hours earlier, snaking around the building on a chilly December night. By Thursday afternoon, more than 430 licenses had been issued in Seattle, where the mood was festive overnight.

“We waited a long time. We’ve been together 35 years, never thinking we’d get a legal marriage. Now I feel so joyous I can’t hardly stand it,” said 85-year-old Pete-e Petersen, who with her partner, 77-year-old Jane Abbott Lighty, were the first to get a license.